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arXiv · 1712.08155

Deforming Lie algebras to Frobenius integrable non-autonomous Hamiltonian systems

Maciej Blaszak·Krzysztof Marciniak·Artur Sergyeyev
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Abstract

Motivated by the theory of Painlev\'e equations and associated hierarchies, we study non-autonomous Hamiltonian systems that are Frobenius integrable. We establish sufficient conditions under which a given finite-dimensional Lie algebra of Hamiltonian vector fields can be deformed to a time-dependent Lie algebra of Frobenius integrable vector fields spanning the same distribution as the original algebra. The results are applied to quasi-St\"ackel systems.

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Maciej Blaszak, Krzysztof Marciniak, Artur Sergyeyev. 2017-12-21. Deforming Lie algebras to Frobenius integrable non-autonomous Hamiltonian systems. https://doi.org/10.1016/s0034-4877(21)00028-8

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